1. Import libraries and dataset¶

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns
from sklearn.model_selection import GridSearchCV,RandomizedSearchCV
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.pipeline import Pipeline
from sklearn.linear_model  import LogisticRegression
from sklearn.naive_bayes import MultinomialNB,GaussianNB
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import SVC,LinearSVC
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier,AdaBoostClassifier,BaggingClassifier
from sklearn.metrics import f1_score, classification_report, confusion_matrix,accuracy_score,log_loss,roc_auc_score,precision_score,recall_score
from sklearn.model_selection import KFold, cross_val_score

Data exploration¶

signal_df = pd.read_csv('signal-data.csv')

#Size of the dataset : 1567 rows and 592 columns
signal_df.shape

(1567, 592)

#Datatypes of the columns in dataset
signal_df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1567 entries, 0 to 1566
Columns: 592 entries, Time to Pass/Fail
dtypes: float64(590), int64(1), object(1)
memory usage: 7.1+ MB

#5 point summary 
signal_df.describe()

From the summary above, we can say that most of the columns have high standard deviation from the mean. Also from the count of columns, we have missing values in some of the columns.¶

signal_df.head(5)

2. Data cleansing¶

#Check for null values
signal_df.isnull().sum()

Time          0
0             6
1             7
2            14
3            14
             ..
586           1
587           1
588           1
589           1
Pass/Fail     0
Length: 592, dtype: int64

#Dropping null values.
signal_processed_df=signal_df.dropna(axis='columns')

signal_processed_df.dropna()

#Check for null values after dropping null values
signal_processed_df.isnull().sum()

Time         0
20           0
86           0
87           0
88           0
113          0
114          0
115          0
116          0
117          0
119          0
120          0
156          0
221          0
222          0
223          0
248          0
249          0
250          0
251          0
252          0
254          0
255          0
291          0
359          0
360          0
361          0
386          0
387          0
388          0
389          0
390          0
392          0
393          0
429          0
493          0
494          0
495          0
520          0
521          0
522          0
523          0
524          0
526          0
527          0
570          0
571          0
572          0
573          0
574          0
575          0
576          0
577          0
Pass/Fail    0
dtype: int64

signal_processed_df.isnull().values.any()

False

Since there are no more null values, we can proceed further.¶

#Check for columns that have few values 
unique_count=signal_processed_df.nunique()
unique_count

Time         1534
20            552
86            472
87            249
88            973
113           468
114            20
115          1567
116           136
117          1527
119           249
120          1269
156           722
221           408
222           178
223           973
248           426
249            23
250          1566
251           143
252          1533
254           291
255          1317
291           354
359           215
360            97
361           972
386           191
387            22
388          1564
389            92
390          1458
392           109
393           953
429          1542
493           572
494           894
495           964
520          1536
521             9
522          1562
523          1040
524          1543
526          1514
527          1549
570           814
571           811
572           518
573           754
574           830
575           599
576           820
577           851
Pass/Fail       2
dtype: int64

#Drop the columns that have single values
to_del = [i for i,v in enumerate(unique_count) if v == 1]
to_del

[]

signal_processed_df.drop(columns=to_del,axis=1)

signal_processed_df.drop(to_del, axis=1)
print(signal_processed_df.shape)

(1567, 54)

signal_processed_df.drop('Time',axis=1,inplace=True)

C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\pandas\core\frame.py:3997: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  errors=errors,

3. Data analysis & visualisation:¶

#Correlation between variables
signal_corr = signal_processed_df.corr()

signal_corr

#heatmap
sns.heatmap(signal_corr,annot=True)

<matplotlib.axes._subplots.AxesSubplot at 0x2156597ac48>

From the correlation matrix above, we can say that majority of the variables are independent of each other. Variables 572 to 575 have high correlation with variable 575,574,576,572.¶

#Distribution of variables
signal_processed_df.hist(stacked=False, bins=100, figsize=(12,30));

#Pairplot
sns.pairplot(signal_processed_df)

<seaborn.axisgrid.PairGrid at 0x21568b94f88>

From the pairplot above , we can see scattered plot with less or no correlation for most of the variables. Whereas for some , we can see positive correlation.¶

From the distribution represented in histogram above, some variables are negatively skewed and some are positively skewed. We will handle negatively skewed data by performing squared function. For positively skewed data, we will perform logarithmic function¶

#retrieving negatively skewed variable indices and performing squared function
skew_ind=signal_processed_df.iloc[:,:-1]

to_skew_neg = skew_ind.skew().index[(skew_ind.skew() < -1)]

signal_processed_df.loc[:,to_skew_neg]=(signal_processed_df[to_skew_neg])**2
to_skew_neg

Index([], dtype='object')

signal_processed_df.iloc[:,:-1].skew()

C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\pandas\core\nanops.py:960: RuntimeWarning: overflow encountered in multiply
  adjusted3 = adjusted2 * adjusted
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\pandas\core\nanops.py:972: RuntimeWarning: overflow encountered in power
  result = (count * (count - 1) ** 0.5 / (count - 2)) * (m3 / m2 ** 1.5)

20     -0.825134
86     -0.334554
87     -0.975940
88     -0.272824
113    -0.905260
114          NaN
115    -0.271651
116    -0.316694
117          NaN
119    -0.614053
120     0.351876
156     0.872707
221     0.759585
222          NaN
223     0.093581
248     0.576730
249          NaN
250    -0.040442
251          NaN
252    27.053379
254     0.585253
255     0.210229
291     0.800852
359    -0.082667
360          NaN
361    -0.223230
386     0.487965
387          NaN
388    -0.015867
389          NaN
390     4.665972
392     0.414009
393     0.102889
429     0.945522
493     0.724469
494    -0.614544
495     0.184196
520     0.617518
521          NaN
522    -0.085700
523     6.924957
524     3.635378
526     0.716253
527     0.181975
570          NaN
571    -0.562176
572     3.981499
573    -0.093918
574    -0.959446
575          NaN
576    -0.802692
577     0.772584
dtype: float64

#retrieving positively skewed variable indices and performing logarithmic function
to_skew_pos = signal_processed_df.iloc[:,:-1].skew().index[signal_processed_df.iloc[:,:-1].skew() > 1]
signal_processed_df.loc[:,to_skew_pos]=np.log(signal_processed_df[to_skew_pos])
to_skew_pos

Index([], dtype='object')

signal_processed_df.iloc[:,:-1].skew()

20    -0.825134
86    -0.334554
87    -0.975940
88    -0.272824
113   -0.905260
115   -0.271651
116   -0.316694
119   -0.614053
120    0.351876
156    0.872707
221    0.759585
223    0.093581
248    0.576730
250   -0.040442
254    0.585253
255    0.210229
291    0.800852
359   -0.082667
361   -0.223230
386    0.487965
388   -0.015867
392    0.414009
393    0.102889
429    0.945522
493    0.724469
495    0.184196
520    0.617518
522   -0.085700
526    0.716253
527    0.181975
571   -0.562176
577    0.772584
dtype: float64

#Distribution of target class in original dataset
sns.countplot(signal_processed_df['Pass/Fail'])

<matplotlib.axes._subplots.AxesSubplot at 0x21565747408>

The Pass - Fail ratio is highly imbalanced¶

signal_processed_df.astype(np.float)

Post handling skewness, we will see if we have infinity or null values¶

signal_processed_df.replace([np.inf,-np.inf], np.NaN,inplace=True)
signal_processed_df.dropna(axis='columns',inplace=True)

C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\pandas\core\frame.py:4172: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  method=method,
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\ipykernel_launcher.py:2: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy

signal_processed_df.shape

(1567, 33)

#sns.pairplot(signal_processed_df)

#Distribution of variables post cleaning
signal_processed_df.hist(stacked=False, bins=100, figsize=(12,30));

4. Data Pre-processing¶

#predictors and target variables

X_signal_processed=signal_processed_df.iloc[:,:-1]
Y_signal = signal_processed_df['Pass/Fail']
X_signal_processed.head(5)

signal_processed_df['Pass/Fail'].value_counts()

-1    1463
 1     104
Name: Pass/Fail, dtype: int64

#scale data
#scale=StandardScaler()
#std_columns=X_signal_processed.columns
#scale.fit(X_signal_processed)

#X_signal_processed=scale.transform(X_signal_processed)
#X_signal_processed_df=pd.DataFrame(X_signal_processed,columns=std_columns)

#Since the target class is imbalanced, we will perform oversampling using randomOverSampler.
from imblearn.under_sampling import TomekLinks,ClusterCentroids,RandomUnderSampler
from imblearn.over_sampling import SMOTE,RandomOverSampler
#tomekLink= TomekLinks()
#undersampling training set
#cc=ClusterCentroids()
#rus=RandomUnderSampler(sampling_strategy='auto')
#from imblearn.combine import SMOTETomek
#smt = SMOTETomek(sampling_strategy=0.1)
ros =RandomOverSampler(sampling_strategy='auto')
X_smt, y_smt = ros.fit_sample(X_signal_processed, Y_signal)

#X_ros,y_ros =ros.fit_sample(X_test,y_test)

X_smt.shape

(2926, 32)

#Split the data into train-test sets in 70:30 ratio
from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test= train_test_split(X_smt,y_smt,random_state=30,test_size=0.30)

#Analysing the distribution of rows in train and test sets
print("no of rows in training set :",X_train.shape[0])
print("no of rows in testing set :",X_test.shape[0])

no of rows in training set : 2048
no of rows in testing set : 878

print("distribution of target class in training set :\n", y_train.value_counts())
print("distribution of target class in testing set :\n", y_test.value_counts())

distribution of target class in training set :
 -1    1027
 1    1021
Name: Pass/Fail, dtype: int64
distribution of target class in testing set :
  1    442
-1    436
Name: Pass/Fail, dtype: int64

From the count above for target class, we can say that it is fairly balanced after applying RandomOverSampler of oversampling¶

#statistical character post processing
signal_processed_df.describe()

#training data summary
X_train.describe()

X_test.describe()

For training and original dataset, we can say that statistical characteristics are similar whereas for test set it is slightly lesser.¶

#print("Distribution of target class for training set post undersampling:\n",y_smt.value_counts())
#print("Distribution of target class for test set post oversampling:\n",pd.Series(y_ros).value_counts())

5.Model training,testing and tuning¶

#Initialise each algorithm and add it to model disctionary
logRegression=LogisticRegression(penalty='l1',solver='saga')
multiNomialNB =MultinomialNB()
gaussianNB=GaussianNB()
svm=SVC(C=1.0,kernel='poly')
decisionCl=DecisionTreeClassifier(criterion='entropy',max_depth=20,max_leaf_nodes=10)
randomForest = RandomForestClassifier(n_estimators=15,criterion='entropy',max_depth=20)
models={"logisticRegression ":logRegression,"gaussianNB":gaussianNB,"svm":svm,"decisionTree":decisionCl,"randomForest":randomForest}

#Find out the best possible value of K  for KNN model
error_rate=[]
knn_accuracy =[]
for i in range(1,50):
    knnModel = KNeighborsClassifier(n_neighbors=i,weights = 'distance')
    knnModel.fit(X_train,y_train)
    knn_predict = knnModel.predict(X_test)
    knn_accuracy.append(accuracy_score(y_test,knn_predict))
    error_rate.append(knnModel.score(X_test,y_test))

plt.figure(figsize=(10,6))
plt.plot(range(1,50),error_rate,color='blue', linestyle='dashed', marker='o',markerfacecolor='red', markersize=10)
plt.title('Error Rate vs. K Value')
plt.xlabel('K')
plt.ylabel('Error Rate')

Text(0, 0.5, 'Error Rate')

#Distribution of predicted values
pd.Series(knn_predict).value_counts()

 1    628
-1    250
dtype: int64

knn_accuracy

[0.9555808656036446,
 0.9555808656036446,
 0.9236902050113895,
 0.9225512528473804,
 0.8952164009111617,
 0.8929384965831435,
 0.8712984054669703,
 0.8667425968109339,
 0.8485193621867881,
 0.8473804100227791,
 0.8439635535307517,
 0.8314350797266514,
 0.8337129840546698,
 0.8257403189066059,
 0.8200455580865603,
 0.8211845102505695,
 0.8223234624145785,
 0.8154897494305239,
 0.8223234624145785,
 0.8200455580865603,
 0.816628701594533,
 0.8177676537585421,
 0.816628701594533,
 0.8120728929384966,
 0.8143507972665148,
 0.8132118451025057,
 0.8109339407744874,
 0.806378132118451,
 0.8097949886104784,
 0.8029612756264237,
 0.8052391799544419,
 0.7995444191343963,
 0.8029612756264237,
 0.8006833712984055,
 0.8075170842824602,
 0.8041002277904328,
 0.8029612756264237,
 0.8018223234624146,
 0.8029612756264237,
 0.8018223234624146,
 0.806378132118451,
 0.7995444191343963,
 0.8018223234624146,
 0.8041002277904328,
 0.8018223234624146,
 0.8018223234624146,
 0.7984054669703873,
 0.7938496583143508,
 0.7881548974943052]

#Since at neighbours =10 the  error rate decrease is constant, we will take 10 as the nearest neighbour count.
knnModel= KNeighborsClassifier(n_neighbors=10,weights = 'distance')

#Add KNN model to model dictionary
models["KNNModel"]=knnModel

models

{'logisticRegression ': LogisticRegression(penalty='l1', solver='saga'),
 'gaussianNB': GaussianNB(),
 'svm': SVC(kernel='poly'),
 'decisionTree': DecisionTreeClassifier(criterion='entropy', max_depth=20, max_leaf_nodes=10),
 'randomForest': RandomForestClassifier(criterion='entropy', max_depth=20, n_estimators=15),
 'KNNModel': KNeighborsClassifier(n_neighbors=10, weights='distance')}

#Loop through each model in dictionary, train , predict and find the accuracy of each model 
accuracy_score_test =[]
accuracy_score_train =[]

for model,objct in models.items():
    print(model)
    objct.fit(X_train,y_train)
    model_predict = objct.predict(X_test)
    model_predict_train=objct.predict(X_train)
    #accuracy_score_train.append(accuracy_score(y_train,model_predict_train))
   # accuracy_score_test.append(accuracy_score(y_ros,model_predict))
    print("Accuracy score for training set for model {} is {}".format(model, accuracy_score(y_train,model_predict_train)))
    print("Accuracy score for testing set for model {} is {}".format(model, accuracy_score(y_test,model_predict)))   
    print("AUC score :\n",roc_auc_score(y_test,model_predict))
    #print out the classification report
    print("Classification report:\n",classification_report(y_test,model_predict))
    print(pd.Series(model_predict).value_counts())

logisticRegression 
Accuracy score for training set for model logisticRegression  is 0.5498046875
Accuracy score for testing set for model logisticRegression  is 0.5489749430523918
AUC score :
 0.5490161484494998
Classification report:
               precision    recall  f1-score   support

          -1       0.55      0.56      0.55       436
           1       0.55      0.54      0.55       442

    accuracy                           0.55       878
   macro avg       0.55      0.55      0.55       878
weighted avg       0.55      0.55      0.55       878

-1    444
 1    434
dtype: int64
gaussianNB
Accuracy score for training set for model gaussianNB is 0.63427734375

C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)

Accuracy score for testing set for model gaussianNB is 0.570615034168565
AUC score :
 0.5705871974760264
Classification report:
               precision    recall  f1-score   support

          -1       0.57      0.57      0.57       436
           1       0.57      0.57      0.57       442

    accuracy                           0.57       878
   macro avg       0.57      0.57      0.57       878
weighted avg       0.57      0.57      0.57       878

 1    443
-1    435
dtype: int64
svm
Accuracy score for training set for model svm is 0.5576171875
Accuracy score for testing set for model svm is 0.5375854214123007
AUC score :
 0.537205778571132
Classification report:
               precision    recall  f1-score   support

          -1       0.54      0.48      0.51       436
           1       0.54      0.59      0.56       442

    accuracy                           0.54       878
   macro avg       0.54      0.54      0.54       878
weighted avg       0.54      0.54      0.54       878

 1    488
-1    390
dtype: int64
decisionTree
Accuracy score for training set for model decisionTree is 0.705078125
Accuracy score for testing set for model decisionTree is 0.693621867881549
AUC score :
 0.6918562414380007
Classification report:
               precision    recall  f1-score   support

          -1       0.90      0.43      0.58       436
           1       0.63      0.95      0.76       442

    accuracy                           0.69       878
   macro avg       0.76      0.69      0.67       878
weighted avg       0.76      0.69      0.67       878

 1    667
-1    211
dtype: int64
randomForest
Accuracy score for training set for model randomForest is 1.0
Accuracy score for testing set for model randomForest is 0.9977220956719818
AUC score :
 0.9977064220183487
Classification report:
               precision    recall  f1-score   support

          -1       1.00      1.00      1.00       436
           1       1.00      1.00      1.00       442

    accuracy                           1.00       878
   macro avg       1.00      1.00      1.00       878
weighted avg       1.00      1.00      1.00       878

 1    444
-1    434
dtype: int64
KNNModel
Accuracy score for training set for model KNNModel is 1.0
Accuracy score for testing set for model KNNModel is 0.8473804100227791
AUC score :
 0.8463302752293578
Classification report:
               precision    recall  f1-score   support

          -1       1.00      0.69      0.82       436
           1       0.77      1.00      0.87       442

    accuracy                           0.85       878
   macro avg       0.88      0.85      0.84       878
weighted avg       0.88      0.85      0.84       878

 1    576
-1    302
dtype: int64

Hyperparameter tuning using gridSearchCV and randomSearchCV¶

During training and testing with both type of hyperparameter tuning techniques, it was found out that gridSearchCV took a lot of processing time. Hence we proceeded with RandomSearchCV technique.Below are the observations.¶

#pipeline for each model
pipe_lr = Pipeline([ ('pca', PCA(n_components=5)), ('LogisticReg', logRegression)]) 
pipe_knn=Pipeline([ ('pca', PCA(n_components=7)), ('KNN', knnModel)]) 
pipe_svm=Pipeline([('pca', PCA(n_components=7)), ('SVM', svm)])
pipe_nb=Pipeline([('pca', PCA(n_components=7)), ('NB', gaussianNB)])
pipe_dcl =Pipeline([ ('pca', PCA(n_components=5)), ('DecisionTree', decisionCl)])
pipe_rf =Pipeline([ ('pca', PCA(n_components=5)), ('RandomForest', randomForest)])

#param grid 
param_grid_lr = {'LogisticReg__C':list(range(1,3)),
                'LogisticReg__penalty': ['l1', 'l2'],
                 'LogisticReg__solver':  ['liblinear','saga']
                }

param_grid_knn = {'KNN__n_neighbors': list(range(1,20)),
             'KNN__algorithm': ['auto', 'ball_tree', 'kd_tree' , 'brute'],
             'KNN__weights':['uniform','distance']}


param_grid_svm={'SVM__C':list(range(1,3)),
                'SVM__kernel':['linear', 'poly','rbf']
               }

param_grid_decisionCl = {'DecisionTree__criterion':['gini','entropy'],
                         'DecisionTree__splitter':['best','random'],
                         'DecisionTree__max_depth':list(range(1,200)),
                         'DecisionTree__max_leaf_nodes':list(range(1,200))
                        }

param_grid_rf ={'RandomForest__n_estimators':list(range(1,100)),'RandomForest__criterion':['gini','entropy'],'RandomForest__max_depth':list(range(1,100))}

#Randomised search
rs_lr=  RandomizedSearchCV(pipe_lr,param_grid_lr,n_iter=5,cv=5)
rs_knn = RandomizedSearchCV(pipe_knn,param_grid_knn,n_iter=5,cv=5)
rs_dcl = RandomizedSearchCV(pipe_dcl,param_grid_decisionCl,n_iter=5,cv=5)
rs_svm=GridSearchCV(pipe_svm,param_grid_svm,cv=5)
rs_rf = RandomizedSearchCV(pipe_rf,param_grid_rf,n_iter=5,cv=5)

#grid dictionary
grids = [rs_lr, rs_knn,rs_dcl,rs_rf]
# Dictionary of pipelines and classifier types for ease of reference
grid_dict = {0: 'Logistic Regression', 1: 'KNN',2:'decisionClassifier',3:'RandomForest'}

pipe_dcl.get_params().keys()

dict_keys(['memory', 'steps', 'verbose', 'pca', 'DecisionTree', 'pca__copy', 'pca__iterated_power', 'pca__n_components', 'pca__random_state', 'pca__svd_solver', 'pca__tol', 'pca__whiten', 'DecisionTree__ccp_alpha', 'DecisionTree__class_weight', 'DecisionTree__criterion', 'DecisionTree__max_depth', 'DecisionTree__max_features', 'DecisionTree__max_leaf_nodes', 'DecisionTree__min_impurity_decrease', 'DecisionTree__min_impurity_split', 'DecisionTree__min_samples_leaf', 'DecisionTree__min_samples_split', 'DecisionTree__min_weight_fraction_leaf', 'DecisionTree__random_state', 'DecisionTree__splitter'])

#loop through dictionary for randomSearch and calculate the accuracy, classification report and target distributions
for idx, gs in enumerate(grids):
    print('\nEstimator: %s' % grid_dict[idx])
    # Fit grid search
    gs.fit(X_train, y_train)
    # Best params
    print('Best params: %s' % gs.best_params_)
    # Predict on test data with best params
    y_pred = gs.predict(X_test)
    # Test data accuracy of model with best params
    print('Test set accuracy score for best params: %.3f ' % accuracy_score(y_test, y_pred))
    print('Classification report:\n',classification_report(y_test,y_pred))
    # Track best (highest test accuracy) model
    print("value counts : \n",pd.Series(y_pred).value_counts())

Estimator: Logistic Regression

C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)
C:\Users\AshwiniShivaprasad\anaconda\lib\site-packages\sklearn\linear_model\_sag.py:329: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge
  "the coef_ did not converge", ConvergenceWarning)

Best params: {'LogisticReg__solver': 'liblinear', 'LogisticReg__penalty': 'l1', 'LogisticReg__C': 1}
Test set accuracy score for best params: 0.540 
Classification report:
               precision    recall  f1-score   support

          -1       0.54      0.53      0.53       436
           1       0.54      0.55      0.55       442

    accuracy                           0.54       878
   macro avg       0.54      0.54      0.54       878
weighted avg       0.54      0.54      0.54       878

value counts : 
  1    446
-1    432
dtype: int64

Estimator: KNN
Best params: {'KNN__weights': 'distance', 'KNN__n_neighbors': 3, 'KNN__algorithm': 'kd_tree'}
Test set accuracy score for best params: 0.928 
Classification report:
               precision    recall  f1-score   support

          -1       1.00      0.86      0.92       436
           1       0.88      1.00      0.93       442

    accuracy                           0.93       878
   macro avg       0.94      0.93      0.93       878
weighted avg       0.94      0.93      0.93       878

value counts : 
  1    505
-1    373
dtype: int64

Estimator: decisionClassifier
Best params: {'DecisionTree__splitter': 'best', 'DecisionTree__max_leaf_nodes': 160, 'DecisionTree__max_depth': 160, 'DecisionTree__criterion': 'entropy'}
Test set accuracy score for best params: 0.942 
Classification report:
               precision    recall  f1-score   support

          -1       1.00      0.88      0.94       436
           1       0.90      1.00      0.95       442

    accuracy                           0.94       878
   macro avg       0.95      0.94      0.94       878
weighted avg       0.95      0.94      0.94       878

value counts : 
  1    493
-1    385
dtype: int64

Estimator: RandomForest
Best params: {'RandomForest__n_estimators': 35, 'RandomForest__max_depth': 49, 'RandomForest__criterion': 'gini'}
Test set accuracy score for best params: 0.989 
Classification report:
               precision    recall  f1-score   support

          -1       1.00      0.98      0.99       436
           1       0.98      1.00      0.99       442

    accuracy                           0.99       878
   macro avg       0.99      0.99      0.99       878
weighted avg       0.99      0.99      0.99       878

value counts : 
  1    452
-1    426
dtype: int64

#Naive Bayes pipeline
pipe_nb.fit(X_train,y_train)
pipe_predict =pipe_nb.predict(X_test)
print("Accuracy score:",accuracy_score(y_test,pipe_predict))
print("Classification report:\n",classification_report(y_test,pipe_predict))
print("value counts : \n",pd.Series(pipe_predict).value_counts())

Accuracy score: 0.5592255125284739
Classification report:
               precision    recall  f1-score   support

          -1       0.55      0.59      0.57       436
           1       0.57      0.53      0.55       442

    accuracy                           0.56       878
   macro avg       0.56      0.56      0.56       878
weighted avg       0.56      0.56      0.56       878

value counts : 
 -1    463
 1    415
dtype: int64

Display the results of models¶

1. Without tuning¶

Results for test set¶

Model/metrics	Precision	Recall	AUC	F1	Accuracy	Pass(-1)	Fail(1)
Logistic Regression	0.52	0.56	0.53	0.54	0.53	444	434
K-Nearest Neighbour	1	0.68	0.84	0.81	0.84	576	302
Naive Bayes	0.59	0.60	0.59	0.47	0.65	443	435
svm	0.54	0.58	0.55	0.56	0.55	488	390
Random Forest	1	0.94	0.97	0.97	0.97	444	434
Decision tree	0.66	0.77	0.673	0.68	0.67	667	211

Results for training set¶

Model/metrics	Accuracy
Logistic Regression	0.55
K-Nearest Neighbour	1
Naive Bayes	0.62
svm	0.53
Random Forest	0.98
Decision tree	0.61

2. With tuning¶

Model/metrics	Precision	Recall	F1	Accuracy	Pass(-1)	Fail(1)
Logistic Regression	0.52	0.51	0.52	0.54	446	432
K-Nearest Neighbour	1	0.79	0.88	0.93	505	373
Naive Bayes	0.55	0.58	0.56	0.56	463	415
Random Forest	1	0.98	0.99	0.99	452	426
Decision tree	1	0.88	0.93	0.94	493	385

Model selected:¶

Out of all these cases, since random forest has the maximum accuracy and F1 score, we will pick this for future predictions. The performance of random forest model has found to be consistent for all combination of dataset.

Import the future data file and predict the outcomes using model picked above i.e RandomForest¶

#Loading data and data cleaning
signal_pred=pd.read_excel('Future_predictions.xlsx')

signal_pred.shape

(18, 591)

signal_pred.head(5)

columns_not_drop=signal_processed_df.columns
columns_not_drop=columns_not_drop[:-1]
columns_not_drop

Index(['20', '86', '87', '88', '113', '115', '116', '119', '120', '156', '221',
       '223', '248', '250', '254', '255', '291', '359', '361', '386', '388',
       '392', '393', '429', '493', '495', '520', '522', '526', '527', '571',
       '577'],
      dtype='object')

signal_pred_processed=signal_pred.dropna(axis=1)
signal_pred_processed.shape

(18, 535)

signal_pred_processed.isnull().sum()

Time    0
0       0
1       0
2       0
3       0
       ..
577     0
582     0
583     0
584     0
585     0
Length: 535, dtype: int64

unique_count=signal_pred_processed.nunique()
unique_count

Time    18
0       18
1       18
2       11
3       11
        ..
577     18
582     17
583     18
584     15
585     18
Length: 535, dtype: int64

#Drop the columns that have single values
to_del = [i for i,v in enumerate(unique_count) if v == 1]
to_del

[6,
 14,
 43,
 50,
 53,
 70,
 73,
 95,
 108,
 135,
 143,
 170,
 171,
 178,
 181,
 182,
 183,
 184,
 185,
 186,
 198,
 201,
 217,
 220,
 221,
 222,
 223,
 224,
 225,
 226,
 227,
 228,
 231,
 232,
 233,
 234,
 236,
 243,
 244,
 245,
 246,
 247,
 248,
 249,
 250,
 251,
 252,
 253,
 263,
 271,
 298,
 299,
 300,
 307,
 310,
 311,
 312,
 313,
 314,
 315,
 327,
 330,
 346,
 351,
 352,
 353,
 354,
 355,
 356,
 357,
 360,
 361,
 362,
 363,
 365,
 372,
 373,
 374,
 375,
 376,
 377,
 378,
 379,
 380,
 381,
 382,
 392,
 400,
 427,
 428,
 429,
 436,
 439,
 440,
 441,
 442,
 443,
 444,
 456,
 459,
 475,
 478,
 479,
 480,
 481,
 482,
 483,
 484,
 485,
 486,
 489,
 490,
 491,
 492,
 494,
 501,
 502,
 503,
 504,
 505,
 506,
 507,
 508,
 509,
 510,
 511,
 515,
 516,
 517,
 518]

signal_pred_processed=signal_pred_processed.drop(signal_pred_processed.columns[to_del], axis='columns')

signal_pred_processed.shape

(18, 405)

print(columns_not_drop)

Index(['20', '86', '87', '88', '113', '115', '116', '119', '120', '156', '221',
       '223', '248', '250', '254', '255', '291', '359', '361', '386', '388',
       '392', '393', '429', '493', '495', '520', '522', '526', '527', '571',
       '577'],
      dtype='object')

signal_pred_processed=signal_pred_processed[[20,86,87, 88, 113, 115, 116, 119, 120, 156, 221, 223, 248, 250, 254, 255, 291, 359, 361, 386, 388, 392, 393, 429, 493, 495, 520, 522, 526, 527, 571, 577]]

signal_pred_processed.shape

(18, 32)

signal_pred_processed.isnull().any()

20     False
86     False
87     False
88     False
113    False
115    False
116    False
119    False
120    False
156    False
221    False
223    False
248    False
250    False
254    False
255    False
291    False
359    False
361    False
386    False
388    False
392    False
393    False
429    False
493    False
495    False
520    False
522    False
526    False
527    False
571    False
577    False
dtype: bool

#Predicting for future prediction file using RandomForest model built above.
y_pred= rs_rf.predict(signal_pred_processed)

#Displaying the predictions
y_pred

array([-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
       -1], dtype=int64)

#Distribution of predicted values.
pd.Series(y_pred).value_counts()

-1    18
dtype: int64

6. Conclusion¶

From the results dislayed above, following are the conclusions:

1. Balancing the dataset has helped us predict in a  balanced way. In our case , we can observe that the pass/fail ratio has been balanced for every model.
2.Hyperparameter Tuning techniques like RandomSearchCV has improved the performances for some algorithms like KNN, RandomForest and DecisionTree by selecting the best combination of hyperparameters values . Also it has helped us performed cross validation implicitly.
3.Pipelining technique has helped us perform 2-3 tasks in one run thus reducing the coding complexity.

	0	1	2	3	4	5	6	7	8	9	...	581	582	583	584	585	586	587	588	589	Pass/Fail
count	1561.000000	1560.000000	1553.000000	1553.000000	1553.000000	1553.0	1553.000000	1558.000000	1565.000000	1565.000000	...	618.000000	1566.000000	1566.000000	1566.000000	1566.000000	1566.000000	1566.000000	1566.000000	1566.000000	1567.000000
mean	3014.452896	2495.850231	2200.547318	1396.376627	4.197013	100.0	101.112908	0.121822	1.462862	-0.000841	...	97.934373	0.500096	0.015318	0.003847	3.067826	0.021458	0.016475	0.005283	99.670066	-0.867262
std	73.621787	80.407705	29.513152	441.691640	56.355540	0.0	6.237214	0.008961	0.073897	0.015116	...	87.520966	0.003404	0.017180	0.003720	3.578033	0.012358	0.008808	0.002867	93.891919	0.498010
min	2743.240000	2158.750000	2060.660000	0.000000	0.681500	100.0	82.131100	0.000000	1.191000	-0.053400	...	0.000000	0.477800	0.006000	0.001700	1.197500	-0.016900	0.003200	0.001000	0.000000	-1.000000
25%	2966.260000	2452.247500	2181.044400	1081.875800	1.017700	100.0	97.920000	0.121100	1.411200	-0.010800	...	46.184900	0.497900	0.011600	0.003100	2.306500	0.013425	0.010600	0.003300	44.368600	-1.000000
50%	3011.490000	2499.405000	2201.066700	1285.214400	1.316800	100.0	101.512200	0.122400	1.461600	-0.001300	...	72.288900	0.500200	0.013800	0.003600	2.757650	0.020500	0.014800	0.004600	71.900500	-1.000000
75%	3056.650000	2538.822500	2218.055500	1591.223500	1.525700	100.0	104.586700	0.123800	1.516900	0.008400	...	116.539150	0.502375	0.016500	0.004100	3.295175	0.027600	0.020300	0.006400	114.749700	-1.000000
max	3356.350000	2846.440000	2315.266700	3715.041700	1114.536600	100.0	129.252200	0.128600	1.656400	0.074900	...	737.304800	0.509800	0.476600	0.104500	99.303200	0.102800	0.079900	0.028600	737.304800	1.000000

	Time	0	1	2	3	4	5	6	7	8	...	581	582	583	584	585	586	587	588	589	Pass/Fail
0	2008-07-19 11:55:00	3030.93	2564.00	2187.7333	1411.1265	1.3602	100.0	97.6133	0.1242	1.5005	...	NaN	0.5005	0.0118	0.0035	2.3630	NaN	NaN	NaN	NaN	-1
1	2008-07-19 12:32:00	3095.78	2465.14	2230.4222	1463.6606	0.8294	100.0	102.3433	0.1247	1.4966	...	208.2045	0.5019	0.0223	0.0055	4.4447	0.0096	0.0201	0.0060	208.2045	-1
2	2008-07-19 13:17:00	2932.61	2559.94	2186.4111	1698.0172	1.5102	100.0	95.4878	0.1241	1.4436	...	82.8602	0.4958	0.0157	0.0039	3.1745	0.0584	0.0484	0.0148	82.8602	1
3	2008-07-19 14:43:00	2988.72	2479.90	2199.0333	909.7926	1.3204	100.0	104.2367	0.1217	1.4882	...	73.8432	0.4990	0.0103	0.0025	2.0544	0.0202	0.0149	0.0044	73.8432	-1
4	2008-07-19 15:22:00	3032.24	2502.87	2233.3667	1326.5200	1.5334	100.0	100.3967	0.1235	1.5031	...	NaN	0.4800	0.4766	0.1045	99.3032	0.0202	0.0149	0.0044	73.8432	-1

	Time	20	86	87	88	113	114	115	116	117	...	527	570	571	572	573	574	575	576	577	Pass/Fail
0	2008-07-19 11:55:00	1.4026	2.3895	0.9690	1747.6049	0.9460	0.0	748.6115	0.9908	58.4306	...	6.6926	533.8500	2.1113	8.95	0.3157	3.0624	0.1026	1.6765	14.9509	-1
1	2008-07-19 12:32:00	1.3825	2.3754	0.9894	1931.6464	0.9425	0.0	731.2517	0.9902	58.6680	...	8.8370	535.0164	2.4335	5.92	0.2653	2.0111	0.0772	1.1065	10.9003	-1
2	2008-07-19 13:17:00	1.4123	2.4532	0.9880	1685.8514	0.9231	0.0	718.5777	0.9899	58.4808	...	6.4568	535.0245	2.0293	11.21	0.1882	4.0923	0.0640	2.0952	9.2721	1
3	2008-07-19 14:43:00	1.4011	2.4004	0.9904	1752.0968	0.9564	0.0	709.0867	0.9906	58.6635	...	6.4865	530.5682	2.0253	9.33	0.1738	2.8971	0.0525	1.7585	8.5831	-1
4	2008-07-19 15:22:00	1.3888	2.4530	0.9902	1828.3846	0.9424	0.0	796.5950	0.9908	58.3858	...	6.3745	532.0155	2.0275	8.83	0.2224	3.1776	0.0706	1.6597	10.9698	-1
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
1562	2008-10-16 15:13:00	1.4072	2.3762	0.9861	1869.4215	0.9520	0.0	727.6761	0.9894	58.3514	...	2.6649	536.3418	2.0153	7.98	0.2363	2.6401	0.0785	1.4879	11.7256	-1
1563	2008-10-16 20:49:00	1.3949	2.4880	0.9911	1872.5133	0.9561	0.0	755.7527	0.9899	57.1020	...	6.0192	537.9264	2.1814	5.48	0.3891	1.9077	0.1213	1.0187	17.8379	-1
1564	2008-10-17 05:26:00	1.4256	2.4590	0.9869	1820.3629	0.9488	0.0	704.2686	0.9891	59.2046	...	5.4641	530.3709	2.3435	6.49	0.4154	2.1760	0.1352	1.2237	17.7267	-1
1565	2008-10-17 06:01:00	1.3868	2.3600	0.9796	1627.4714	0.9485	0.0	605.6190	0.9896	58.2686	...	6.5512	534.3936	1.9098	9.13	0.3669	3.2524	0.1040	1.7085	19.2104	-1
1566	2008-10-17 06:07:00	1.4048	2.3701	0.9758	1759.9908	0.9432	0.0	683.5622	0.9893	59.8578	...	4.1651	528.7918	2.0831	6.81	0.4774	2.2727	0.1495	1.2878	22.9183	-1

	Time	20	86	87	88	113	114	115	116	117	...	527	570	571	572	573	574	575	576	577	Pass/Fail
0	2008-07-19 11:55:00	1.4026	2.3895	0.9690	1747.6049	0.9460	0.0	748.6115	0.9908	58.4306	...	6.6926	533.8500	2.1113	8.95	0.3157	3.0624	0.1026	1.6765	14.9509	-1
1	2008-07-19 12:32:00	1.3825	2.3754	0.9894	1931.6464	0.9425	0.0	731.2517	0.9902	58.6680	...	8.8370	535.0164	2.4335	5.92	0.2653	2.0111	0.0772	1.1065	10.9003	-1
2	2008-07-19 13:17:00	1.4123	2.4532	0.9880	1685.8514	0.9231	0.0	718.5777	0.9899	58.4808	...	6.4568	535.0245	2.0293	11.21	0.1882	4.0923	0.0640	2.0952	9.2721	1
3	2008-07-19 14:43:00	1.4011	2.4004	0.9904	1752.0968	0.9564	0.0	709.0867	0.9906	58.6635	...	6.4865	530.5682	2.0253	9.33	0.1738	2.8971	0.0525	1.7585	8.5831	-1
4	2008-07-19 15:22:00	1.3888	2.4530	0.9902	1828.3846	0.9424	0.0	796.5950	0.9908	58.3858	...	6.3745	532.0155	2.0275	8.83	0.2224	3.1776	0.0706	1.6597	10.9698	-1
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
1562	2008-10-16 15:13:00	1.4072	2.3762	0.9861	1869.4215	0.9520	0.0	727.6761	0.9894	58.3514	...	2.6649	536.3418	2.0153	7.98	0.2363	2.6401	0.0785	1.4879	11.7256	-1
1563	2008-10-16 20:49:00	1.3949	2.4880	0.9911	1872.5133	0.9561	0.0	755.7527	0.9899	57.1020	...	6.0192	537.9264	2.1814	5.48	0.3891	1.9077	0.1213	1.0187	17.8379	-1
1564	2008-10-17 05:26:00	1.4256	2.4590	0.9869	1820.3629	0.9488	0.0	704.2686	0.9891	59.2046	...	5.4641	530.3709	2.3435	6.49	0.4154	2.1760	0.1352	1.2237	17.7267	-1
1565	2008-10-17 06:01:00	1.3868	2.3600	0.9796	1627.4714	0.9485	0.0	605.6190	0.9896	58.2686	...	6.5512	534.3936	1.9098	9.13	0.3669	3.2524	0.1040	1.7085	19.2104	-1
1566	2008-10-17 06:07:00	1.4048	2.3701	0.9758	1759.9908	0.9432	0.0	683.5622	0.9893	59.8578	...	4.1651	528.7918	2.0831	6.81	0.4774	2.2727	0.1495	1.2878	22.9183	-1

	20	86	87	88	113	114	115	116	117	119	...	527	570	571	572	573	574	575	576	577	Pass/Fail
20	1.000000	0.050032	0.055319	-0.065107	0.024664	-0.031431	0.025619	0.046091	0.019993	-0.001825	...	-0.046716	-0.000205	-0.021436	-0.025429	-0.020366	-0.022118	-0.025880	-0.024596	-0.026571	0.023253
86	0.050032	1.000000	0.031000	-0.003571	0.014488	-0.024863	-0.014257	0.028356	0.014794	-0.001545	...	-0.043544	-0.006474	-0.012701	0.033938	0.052387	0.029529	0.056517	0.032696	0.053237	0.024974
87	0.055319	0.031000	1.000000	-0.061580	0.106847	-0.042029	-0.052125	-0.003568	-0.033015	-0.005589	...	-0.026713	0.025988	-0.031415	0.012448	0.028469	0.007819	0.027971	0.009253	0.035851	-0.030422
88	-0.065107	-0.003571	-0.061580	1.000000	0.100660	0.009750	0.116503	0.003269	0.010875	0.026516	...	-0.003777	-0.022459	0.020736	-0.026952	-0.017848	-0.026170	-0.016366	-0.024665	-0.021203	0.026865
113	0.024664	0.014488	0.106847	0.100660	1.000000	-0.285839	-0.041832	0.056295	0.019973	0.025750	...	-0.047714	0.068486	-0.135673	0.000455	-0.019055	-0.006844	-0.033629	-0.005915	0.010921	0.001328
114	-0.031431	-0.024863	-0.042029	0.009750	-0.285839	1.000000	-0.005372	-0.046802	-0.007135	-0.034011	...	0.005271	0.009354	0.048395	-0.013727	-0.006772	-0.013679	0.003335	-0.013976	-0.013607	0.068655
115	0.025619	-0.014257	-0.052125	0.116503	-0.041832	-0.005372	1.000000	0.000273	-0.005960	0.042306	...	0.001207	-0.019066	-0.024488	0.030013	0.036066	0.027323	0.040390	0.030523	0.041202	-0.043654
116	0.046091	0.028356	-0.003568	0.003269	0.056295	-0.046802	0.000273	1.000000	-0.070123	-0.010319	...	0.058791	0.006897	-0.096214	0.024899	-0.016263	0.024734	-0.010626	0.023093	0.005018	-0.012912
117	0.019993	0.014794	-0.033015	0.010875	0.019973	-0.007135	-0.005960	-0.070123	1.000000	-0.012869	...	-0.033664	-0.003324	-0.017164	-0.002197	-0.009813	-0.002848	-0.009048	-0.002175	-0.006304	-0.016720
119	-0.001825	-0.001545	-0.005589	0.026516	0.025750	-0.034011	0.042306	-0.010319	-0.012869	1.000000	...	0.073035	-0.004159	-0.031574	-0.013043	-0.016697	-0.014020	-0.012939	-0.013427	-0.009130	0.005612
120	-0.025870	-0.025436	0.018598	-0.029887	-0.064379	0.026087	-0.020330	-0.033373	-0.006748	-0.314995	...	0.095576	-0.008374	0.017703	0.021675	-0.004254	0.023976	-0.008324	0.024473	-0.009210	-0.020277
156	-0.480092	-0.024185	0.000587	0.015746	0.007298	0.003831	-0.009939	-0.014849	0.011803	0.028717	...	0.050375	-0.001302	0.019842	0.005135	0.043805	0.004994	0.059437	0.004463	0.030379	0.002154
221	0.035726	-0.094688	0.013984	-0.048973	-0.050905	0.034508	-0.001386	-0.049050	0.006011	0.003222	...	-0.038337	-0.018657	0.022123	0.053900	0.046349	0.055708	0.048524	0.055600	0.038010	0.021609
222	-0.036882	-0.029315	-0.666112	-0.012177	-0.056095	0.009713	0.056708	0.009592	0.001133	0.010617	...	0.007053	-0.035865	0.024664	-0.002391	-0.014555	0.002912	-0.009121	0.001792	-0.019954	0.031294
223	0.035709	0.033215	-0.184025	-0.063731	-0.018882	-0.016422	-0.024287	0.001550	0.004167	-0.002402	...	-0.056952	0.000965	-0.011732	0.002504	-0.001675	0.002391	0.001668	0.001301	0.004871	-0.001068
248	-0.028265	-0.009478	-0.027136	0.022275	-0.462054	0.701354	-0.016583	-0.030914	-0.003855	-0.033057	...	0.001519	-0.026059	0.040836	-0.004445	-0.002235	-0.001659	0.008389	-0.002144	-0.009722	0.008912
249	-0.033351	-0.028947	-0.036359	0.021289	-0.295515	0.977050	-0.011662	-0.052847	-0.008050	-0.032172	...	-0.004823	0.009649	0.042595	-0.013239	-0.005529	-0.013191	0.004067	-0.013469	-0.011710	0.066478
250	-0.001040	-0.001482	0.017542	0.084469	-0.015657	0.024117	0.020353	0.033181	0.026008	0.024171	...	-0.053820	-0.016350	-0.034609	0.017044	-0.004188	0.015737	-0.002322	0.016874	0.004559	0.006964
251	-0.008267	-0.011079	0.008984	0.014247	0.004538	-0.005007	0.010882	-0.500774	0.208033	0.042319	...	-0.049977	0.009655	0.018542	-0.015878	-0.009009	-0.016023	-0.007426	-0.015982	-0.013056	-0.010315
252	0.020560	0.012529	-0.033380	0.014709	0.016530	-0.001406	-0.003153	-0.150705	0.986193	-0.013886	...	-0.037093	0.001676	-0.011364	-0.005791	-0.009891	-0.005905	-0.009395	-0.005894	-0.008353	-0.006634
254	0.004270	-0.016767	0.002600	-0.020535	-0.042144	0.044471	-0.037003	0.021205	0.002270	-0.795787	...	0.120521	-0.004231	0.066721	0.026515	0.024411	0.028117	0.025388	0.028107	0.013087	-0.021509
255	-0.047036	-0.044394	-0.025703	-0.006563	-0.051747	0.006875	0.000931	0.056109	-0.033801	0.053133	...	0.997831	-0.001087	0.110017	0.022886	0.002827	0.028420	0.022094	0.026680	-0.017745	-0.011730
291	-0.486590	-0.023837	0.002259	0.012306	0.004996	0.003199	-0.012179	-0.014742	0.009742	0.021806	...	0.046912	0.000080	0.021581	0.005496	0.043071	0.005266	0.058470	0.004658	0.029990	0.000007
359	0.040344	-0.090202	0.022785	-0.050066	-0.042738	0.036278	0.004214	-0.048648	0.008959	0.007212	...	-0.055379	-0.025933	0.019865	0.054428	0.055168	0.056947	0.056926	0.056607	0.046606	0.033077
360	-0.037356	-0.030128	-0.690430	-0.010635	-0.057063	0.009287	0.063079	0.010452	0.001306	0.011922	...	0.008175	-0.032558	0.018659	-0.003721	-0.016447	0.001051	-0.011477	0.000014	-0.020803	0.038608
361	0.043506	0.034337	-0.186550	-0.037648	-0.015730	-0.006272	-0.014255	0.003708	-0.000094	-0.008515	...	-0.047953	-0.001907	-0.014840	0.011358	0.005154	0.011294	0.010484	0.010288	0.012923	-0.004971
386	-0.028633	-0.007842	-0.026420	0.020615	-0.461221	0.697562	-0.021760	-0.028299	-0.003257	-0.030943	...	-0.002350	-0.022088	0.036144	-0.004357	-0.002952	-0.001635	0.007510	-0.002460	-0.009458	0.008212
387	-0.033328	-0.028726	-0.036401	0.020506	-0.295545	0.978660	-0.011260	-0.052732	-0.008047	-0.032175	...	-0.004338	0.009652	0.042901	-0.013259	-0.005653	-0.013209	0.003982	-0.013490	-0.011864	0.066315
388	-0.006756	0.012244	0.015236	0.094324	-0.025518	0.036863	0.006647	0.028367	0.033001	0.027856	...	-0.059447	-0.014040	-0.029975	0.013263	-0.003690	0.013122	-0.000915	0.012834	0.004772	0.019723
389	-0.008013	-0.010957	0.009095	0.014363	0.004956	-0.004716	0.010860	-0.495624	0.207895	0.042254	...	-0.050032	0.009728	0.017785	-0.015466	-0.008797	-0.015609	-0.007202	-0.015580	-0.012691	-0.010372
390	0.020230	0.012624	-0.033452	0.014787	0.016410	-0.001608	-0.003359	-0.150415	0.986234	-0.014036	...	-0.037297	0.001687	-0.011406	-0.005937	-0.010102	-0.006054	-0.009604	-0.006046	-0.008538	-0.006805
392	0.011899	-0.021890	0.012117	-0.027125	-0.049537	0.044315	-0.040157	0.022692	0.005072	-0.786370	...	0.119740	-0.002722	0.068766	0.027564	0.027336	0.029321	0.028653	0.029100	0.014539	-0.021268
393	-0.045068	-0.041500	-0.028994	-0.005397	-0.062275	0.019206	-0.002040	0.058764	-0.035212	0.022361	...	0.981828	0.003653	0.124244	0.022105	0.004639	0.026793	0.024246	0.025619	-0.018353	-0.003346
429	-0.490262	-0.024608	0.000886	0.014120	0.005998	0.003269	-0.007623	-0.014416	0.009915	0.027705	...	0.051199	-0.000686	0.024671	0.004021	0.046718	0.003838	0.063353	0.003398	0.031586	0.000275
493	0.033054	-0.138023	0.012088	-0.048142	-0.051803	0.036174	-0.001609	-0.049814	0.005315	0.002799	...	-0.035344	-0.017544	0.023735	0.051172	0.043311	0.053146	0.045353	0.052911	0.034694	0.019420
494	-0.036874	-0.029911	-0.677319	-0.013591	-0.054756	0.007912	0.060111	0.010613	0.001017	0.011676	...	0.007017	-0.032042	0.020355	-0.003361	-0.015688	0.001396	-0.010575	0.000344	-0.020297	0.035182
495	0.037812	0.031144	-0.182408	-0.129776	-0.024838	-0.016103	-0.034123	0.002018	0.003589	-0.004871	...	-0.053074	0.002131	-0.012245	0.004173	0.000152	0.004011	0.003778	0.002885	0.006519	-0.003532
520	-0.028068	-0.009157	-0.025481	0.023494	-0.459774	0.698559	-0.012841	-0.030124	-0.004070	-0.033609	...	-0.000060	-0.024243	0.038910	-0.004874	-0.002480	-0.002217	0.007880	-0.002699	-0.009651	0.007691
521	-0.036054	-0.040938	0.003335	-0.021524	-0.261069	0.606741	0.020500	-0.021769	-0.008197	-0.030059	...	0.018433	0.004552	0.046446	-0.004062	0.004157	-0.003878	0.014788	-0.004547	-0.002178	0.036722
522	-0.007499	-0.000712	0.019417	0.069434	0.002334	0.025102	-0.123783	0.032780	0.027453	0.020292	...	-0.053266	-0.014240	-0.033600	0.013424	-0.008386	0.012473	-0.006858	0.013245	-0.000141	0.013677
523	-0.008447	-0.011536	0.009296	0.013958	0.004581	-0.004909	0.010731	-0.495068	0.201033	0.042226	...	-0.049975	0.009665	0.018676	-0.015536	-0.008837	-0.015673	-0.007190	-0.015640	-0.012852	-0.010401
524	0.019522	0.009908	-0.032697	0.017311	0.014159	0.000792	-0.001246	-0.187591	0.978643	-0.011759	...	-0.043273	0.003212	-0.004323	-0.007136	-0.009400	-0.007340	-0.009941	-0.007283	-0.009246	-0.005837
526	0.003283	-0.015226	0.001353	-0.019670	-0.040447	0.043962	-0.036525	0.021294	0.002296	-0.813955	...	0.118955	-0.003672	0.065617	0.026038	0.023694	0.027615	0.024399	0.027608	0.012581	-0.021536
527	-0.046716	-0.043544	-0.026713	-0.003777	-0.047714	0.005271	0.001207	0.058791	-0.033664	0.073035	...	1.000000	0.000036	0.111009	0.021502	0.003734	0.026855	0.023573	0.025069	-0.016891	-0.010425
570	-0.000205	-0.006474	0.025988	-0.022459	0.068486	0.009354	-0.019066	0.006897	-0.003324	-0.004159	...	0.000036	1.000000	-0.095755	-0.274167	-0.288580	-0.307529	-0.316960	-0.360498	-0.247655	-0.001656
571	-0.021436	-0.012701	-0.031415	0.020736	-0.135673	0.048395	-0.024488	-0.096214	-0.017164	-0.031574	...	0.111009	-0.095755	1.000000	-0.151217	0.096217	-0.138441	0.133902	-0.136232	-0.121115	-0.019353
572	-0.025429	0.033938	0.012448	-0.026952	0.000455	-0.013727	0.030013	0.024899	-0.002197	-0.013043	...	0.021502	-0.274167	-0.151217	1.000000	0.787710	0.993689	0.775835	0.994772	0.863768	-0.032233
573	-0.020366	0.052387	0.028469	-0.017848	-0.019055	-0.006772	0.036066	-0.016263	-0.009813	-0.016697	...	0.003734	-0.288580	0.096217	0.787710	1.000000	0.781319	0.980265	0.790026	0.957874	-0.051873
574	-0.022118	0.029529	0.007819	-0.026170	-0.006844	-0.013679	0.027323	0.024734	-0.002848	-0.014020	...	0.026855	-0.307529	-0.138441	0.993689	0.781319	1.000000	0.774716	0.991738	0.851784	-0.034713
575	-0.025880	0.056517	0.027971	-0.016366	-0.033629	0.003335	0.040390	-0.010626	-0.009048	-0.012939	...	0.023573	-0.316960	0.133902	0.775835	0.980265	0.774716	1.000000	0.780840	0.928311	-0.052731
576	-0.024596	0.032696	0.009253	-0.024665	-0.005915	-0.013976	0.030523	0.023093	-0.002175	-0.013427	...	0.025069	-0.360498	-0.136232	0.994772	0.790026	0.991738	0.780840	1.000000	0.859278	-0.028488
577	-0.026571	0.053237	0.035851	-0.021203	0.010921	-0.013607	0.041202	0.005018	-0.006304	-0.009130	...	-0.016891	-0.247655	-0.121115	0.863768	0.957874	0.851784	0.928311	0.859278	1.000000	-0.049633
Pass/Fail	0.023253	0.024974	-0.030422	0.026865	0.001328	0.068655	-0.043654	-0.012912	-0.016720	0.005612	...	-0.010425	-0.001656	-0.019353	-0.032233	-0.051873	-0.034713	-0.052731	-0.028488	-0.049633	1.000000

	20	86	87	88	113	114	115	116	117	119	...	522	526	527	571	573	574	575	576	577	Pass/Fail
0	14.978581	2.3895	0.365057	1747.6049	0.894916	-inf	748.6115	0.008807	NaN	0.728539	...	3.380328	0.5064	6.6926	4.457588	NaN	-2.183797	NaN	-0.660277	0.995017	-1.0
1	13.345078	2.3754	0.711051	1931.6464	0.888306	-inf	731.2517	0.006459	NaN	0.646427	...	3.273250	0.8832	8.8370	5.921922	NaN	NaN	NaN	-2.290638	0.870787	-1.0
2	15.827622	2.4532	0.679551	1685.8514	0.852114	-inf	718.5777	0.005530	NaN	0.691409	...	2.676167	0.6451	6.4568	4.118058	NaN	-1.070152	NaN	-0.301580	0.800660	1.0
3	14.850910	2.4004	0.734413	1752.0968	0.914701	-inf	709.0867	0.007942	NaN	0.679061	...	2.585498	0.7404	6.4865	4.101840	NaN	-2.784450	NaN	-0.571884	0.765373	-1.0
4	13.839413	2.4530	0.729682	1828.3846	0.888118	-inf	796.5950	0.008807	NaN	0.545227	...	2.930228	2.2181	6.3745	4.110756	NaN	-1.930505	NaN	-0.679961	0.873444	-1.0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
1562	15.376115	2.3762	0.638956	1869.4215	0.906304	-inf	727.6761	0.004270	NaN	0.552521	...	2.016888	1.2587	2.6649	4.061434	NaN	NaN	NaN	-0.922898	0.900882	-1.0
1563	14.333247	2.4880	0.751206	1872.5133	0.914127	-inf	755.7527	0.005530	NaN	0.730921	...	1.846737	0.4512	6.0192	4.758506	NaN	NaN	NaN	-3.988510	1.058250	-1.0
1564	17.060097	2.4590	0.655754	1820.3629	0.900221	-inf	704.2686	0.003656	NaN	0.685771	...	2.813059	0.4867	5.4641	5.491992	NaN	NaN	NaN	-1.600086	1.056078	-1.0
1565	13.680774	2.3600	0.517084	1627.4714	0.899652	-inf	605.6190	0.004735	NaN	0.729729	...	2.798372	0.3866	6.5512	3.647336	NaN	-1.801809	NaN	-0.624338	1.083652	-1.0
1566	15.167569	2.3701	0.456611	1759.9908	0.889626	-inf	683.5622	0.004055	NaN	0.552521	...	2.880002	1.5629	4.1651	4.339306	NaN	NaN	NaN	-1.374621	1.141651	-1.0

	20	86	87	88	113	115	116	119	120	156	...	393	429	493	495	520	522	526	527	571	577
count	2048.000000	2048.000000	2048.000000	2048.000000	2048.000000	2048.000000	2.048000e+03	2048.000000	2048.000000	2048.000000	...	2048.000000	2048.000000	2048.000000	2048.000000	2048.000000	2048.000000	2048.000000	2048.000000	2048.000000	2048.000000
mean	15.282506	2.404071	0.600454	1809.236452	0.894151	743.502929	6.709960e-03	0.628252	6.308254	-2.992665	...	0.133788	1.272144	2.588938	1.865730	0.746094	2.609278	1.403332	6.368471	4.480653	0.958703
std	1.309072	0.035616	0.158249	53.980465	0.021621	48.136530	3.688959e-03	0.074120	0.122740	0.508752	...	0.036658	0.511466	1.096342	0.301084	0.589476	0.399241	0.908839	1.822974	1.194005	0.146680
min	3.751221	2.242500	0.000286	1627.471400	0.728292	544.025400	1.223724e-26	0.062743	5.720700	-4.500810	...	0.034200	-0.243729	0.833000	0.572109	-1.164432	1.024607	0.171600	2.170000	0.969634	0.420114
25%	14.498482	2.378300	0.435749	1777.200500	0.881345	720.965750	4.269882e-03	0.564569	6.234600	-3.286085	...	0.107100	0.974484	1.686900	1.672168	0.404815	2.351337	0.477100	4.956600	3.925153	0.880803
50%	15.315031	2.406800	0.666469	1809.012900	0.896809	748.960900	7.542124e-03	0.613241	6.312100	-3.022076	...	0.133500	1.247578	2.574000	1.893646	0.800184	2.640378	1.498800	6.328500	4.649414	0.958876
75%	16.144153	2.429200	0.717983	1843.723700	0.906494	773.218100	9.274108e-03	0.701669	6.377100	-2.689719	...	0.158575	1.574122	3.216600	2.066508	1.093935	2.871795	2.138400	7.474400	5.306919	1.029829
max	19.910458	2.555500	0.811656	2105.182300	0.953162	924.531800	2.011958e-02	0.749016	7.522000	0.789184	...	0.299400	5.229055	9.402400	2.774162	4.713797	4.927136	8.203700	14.447900	7.504860	1.520454

	20	86	87	88	113	115	116	119	120	156	...	393	429	493	495	520	522	526	527	571	577
count	878.000000	878.000000	878.000000	878.000000	878.000000	878.000000	8.780000e+02	878.000000	878.000000	878.000000	...	878.000000	878.000000	878.000000	878.000000	878.000000	878.000000	878.000000	878.000000	878.000000	878.000000
mean	15.279469	2.401426	0.592960	1811.532403	0.894086	743.216696	6.615665e-03	0.626634	6.302492	-2.975800	...	0.131964	1.288951	2.541713	1.862517	0.741810	2.617671	1.414249	6.248789	4.435929	0.960850
std	1.265690	0.034806	0.168253	53.613223	0.022501	46.467299	3.692529e-03	0.075956	0.127756	0.494325	...	0.035347	0.495585	1.100866	0.318402	0.618776	0.425294	0.917808	1.747856	1.213062	0.145620
min	10.735231	2.248100	0.000286	1627.471400	0.728804	595.796000	2.927357e-22	0.065049	5.125900	-4.305066	...	0.048800	-0.034488	0.861400	0.775234	-0.963644	0.986227	0.170500	2.274700	0.960792	0.497598
25%	14.434257	2.376375	0.415128	1781.323300	0.882144	722.298825	4.054531e-03	0.562699	6.233775	-3.270169	...	0.106700	0.992622	1.636000	1.674748	0.417805	2.326009	0.452500	4.917600	3.896676	0.892172
50%	15.288918	2.405900	0.662163	1809.539650	0.896052	748.055600	7.162150e-03	0.613241	6.304950	-3.024132	...	0.131400	1.238461	2.403250	1.871456	0.768347	2.639122	1.556800	6.252100	4.566987	0.958070
75%	16.162407	2.425575	0.717983	1846.805500	0.906494	771.472400	9.274108e-03	0.702530	6.379475	-2.715075	...	0.155975	1.548116	3.175825	2.051741	1.059291	2.894176	2.178000	7.390500	5.260142	1.027810
max	19.358346	2.507600	0.803850	1955.882800	0.951600	914.824800	1.554389e-02	0.756372	6.766200	-0.526108	...	0.234900	3.755102	9.402400	4.679281	4.716143	4.667576	7.967700	11.933900	7.504860	1.520454